Burnley goalkeeper Pope has enjoyed a previous spell with York City while Swansea City signed central defender Mawson from Barnsley and Bournemouth midfield player Cook joined the Cherries from Leeds United in July, 2016.
Cook lifted the Under-20 World Cup last year and was rewarded by being called up into the senior squad for the first time in November for a friendly against Brazil at Wembley Stadium.
Barnsley received £5.5m when Mawson signed for Swansea on a four-year deal in August, 2016.
Twenty-five-year-old Pope played on loan for the Minstermen in 2013-14 while with Charlton Athletic.
There are also places in manager Gareth Southgate’s squad for Arsenal’s Jack Wilshere and Danny Welbeck.
Injured Tottenham striker Harry Kane and Chelsea defender Gary Cahill are among those who miss out along with defenders Chris Smalling and Michael Keane.
England squad - Goalkeepers: Joe Hart, Jordan Pickford, Jack Butland, Nick Pope.
Defenders: Kyle Walker, Kieran Tripper, Ryan Bertrand, Danny Rose, John Stones, James Tarkowski, Alfie Mawson, Joe Gomez, Harry Maguire.
Midfield players: Eric Dier, Jack Wilshere, Jordan Henderson, Jake Livermore, Adam Lallana, Alex Oxlade-Chamberlain, Dele Alli, Raheem Sterling, Ashley Young, Jesse Lingard, Lewis Cook.
Strikers: Danny Welbeck, Jamie Vardy, Marcus Rashford